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Question
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.
Literacy rate (in %)No. of cities44−55355−651065−751175−85885−953
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.
Literacy rate (in %)No. of cities44−55355−651065−751175−85885−953
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Solution
The correct option is B 69.43
Literacy rate(in %)45−5555−6565−7575−8585−95Number of cities3101183
Class mark(for 1st class interval)
=upper class limit + lower class limit2=45+552=50
Let the assumed mean(a) be 70 (Choose the number in order to get minimum values of d)
The class size(h) is = 55 – 45 = 10 (Upperclass limit- lower class limit)
Class intervalFrequency(fi)Class mark(xi)di=xi−aui=dihfiui45−55350−20−2−655−651060−10−1−1065−75117000075−85880101885−953902026Total∑fi=35∑fiui=−2Mean(u)=a+(∑fiui∑fi)×h=70+(−235)× 10=(70−0.57)=69.43
69.43
Literacy rate(in %)45−5555−6565−7575−8585−95Number of cities3101183
Class mark(for 1st class interval)
=upper class limit + lower class limit2=45+552=50
Let the assumed mean(a) be 70 (Choose the number in order to get minimum values of d)
The class size(h) is = 55 – 45 = 10 (Upperclass limit- lower class limit)
Class intervalFrequency(fi)Class mark(xi)di=xi−aui=dihfiui45−55350−20−2−655−651060−10−1−1065−75117000075−85880101885−953902026Total∑fi=35∑fiui=−2Mean(u)=a+(∑fiui∑fi)×h=70+(−235)× 10=(70−0.57)=69.43
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